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A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees

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  • Malwina Luczak

    (The University of Manchester)

Abstract

We consider a Markovian model of an SIR epidemic spreading on a contact graph that is drawn uniformly at random from the set of all graphs with n vertices and given vertex degrees. Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014) prove that the evolution of such an epidemic is well approximated by the solution to a simple set of differential equations, thus providing probabilistic underpinnings to the works of Miller (J Math Biol 62(3):349–358, 2011) and Volz (J Math Biol 56(3):293–310, 2008). The present paper provides an additional probabilistic interpretation of the limiting deterministic functions in Janson, Luczak and Windridge (Random Struct Alg 45(4):724–761, 2014), thus clarifying further the connection between their results and the results of Miller and Volz.

Suggested Citation

  • Malwina Luczak, 2024. "A Note on the Markovian SIR Epidemic on a Random Graph with Given Degrees," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1039-1051, June.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-024-01320-w
    DOI: 10.1007/s10959-024-01320-w
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